No, the firmware cannot be built on Windows. Generally building a Linux kernel on Windows usually doesn't work. Building the firmware is only necessary if you want to create something persistent on the device or change around the system in any way. Built firmware releases that can be just copied over to the device are available here: https://github.com/analogdevicesinc/plutosdr-fw/releases

Streaming data to and from the transceiver can be done both remotely or on the device. Most users tend to use applications like MATLAB/Simulink, GNU Radio or others (See info.html on the device itself.)

We need to implement transmitter-receiver algorithms on the device itself rather than a remote solution. After building firmware image, how should I incorparate the necessary code? Should it be written in C?

Thank you for your clarification. Regarding USB OTG, for example if we want to execute a C code that calculates FFT of sampled waveform and updates oscillator frequency accordingly, can we just include C code with the USB memory and refer it with a shell script? Thanks in advance